Hermitian curvature flow

  • Gang Tian

    Princeton University, USA
  • Jeffrey Streets

    Princeton University, USA


We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics with negative or zero first Chern class.

Cite this article

Gang Tian, Jeffrey Streets, Hermitian curvature flow. J. Eur. Math. Soc. 13 (2011), no. 3, pp. 601–634

DOI 10.4171/JEMS/262